Jon AS and Jerry LRC,
JAS
A familiar logical triplet is Term, Proposition, Argument. In order
to make this a division of all signs, the first two members have
to be much widened. (CP 4.538; 1906)
If term and proposition were likewise synonymous with Seme and Pheme,
respectively, then why did Peirce state plainly that the latter
require a "much widened" denotation?
I agree with Peirce: "the first two members have to be much widened."
Therefore, take Peirce's advice: Widen the senses of those two words.
Then you can discard the triad seme/pheme/delome as superfluous.
That is the normal way that language develops. As science,
technology, and culture change, people take the old words,
and broaden them to include the new options.
Just look at the they way Newton's words mass, energy, momentum,
space, and time changed during the past two centuries.
Today, most phones don't look like the telephones of the 1970s, and
they have more computer power than the supercomputers of those days.
JLRC
[JFS] Peirce explicitly said that an icon plus one or more indices
can be used to state a proposition. An icon with N-points (pegs)
where an index may be attached represents an N-adic relation.
The source of this assertion would be appreciated.
See below for some related quotations. There are others, but this
selection is enough to show that Peirce did not need the words
seme/pheme/delome to talk about reasoning with and about images.
Basic principle: I hope that we can make Peirce's ideas more widely
known and used in the 21st c. Unusual words that Peirce rarely used
himself are not likely to attract new readers. I believe that it's
not useful to revive those words for any purpose other than making
a scholarly comment about a particular MS in which they occur.
John
____________________________________________________________________
A proposition is a sign which separately indicates its object. Thus,
a portrait with the name of the original below it is a proposition.
It asserts that if anybody looks at it, he can form a reasonably
correct idea of how the original looked. (CP 5.569)
All necessary reasoning without exception is diagrammatic. That is,
we construct an icon of our hypothetical state of things and proceed
to observe it. This observation leads us to suspect that something is
true, which we may or may not be able to formulate with precision,
and we proceed to inquire whether it is true or not. For this purpose
it is necessary to form a plan of investigation, and this is the most
difficult part of the whole operation. We not only have to select the
features of the diagram which it will be pertinent to pay attention to,
but it is also of great importance to return again and again to certain
features. (EP 2:212)
A Diagram is mainly an Icon, and an Icon of intelligible relations...
Now since a diagram, though it will ordinarily have Symbolide Features,
as well as features approaching the nature of Indices, is nevertheless
in the main an Icon of the forms of relations in the constitution of
its Object, the appropriateness of it for the representation of
necessary inference is easily seen. [CP 4.531]
all deductive reasoning, even simple syllogism, involves an element
of observation; namely deduction consists in constructing an icon
or diagram the relation of whose parts shall present a complete analogy
with those of the parts of the object of reasoning, of experimenting
upon this image in the imagination, and of observing the result so as
to discover unnoticed and hidden relations among the parts. [CP 3.363]
The word diagram is here used in the peculiar sense of a concrete, but
possibly changing, mental image of such a thing as it represents. A
drawing or model may be employed to aid the imagination; but the
essential thing to be performed is the act of imagining. Mathematical
diagrams are of two kinds; 1st, the geometrical, which are composed of
lines (for even the image of a body having a curved surface without
edges, what is mainly seen by the mind’s eye as it is turned about, is
its generating lines, such as its varying outline); and 2nd, the
algebraical, which are arrays of letters and other characters whose
interrelations are represented partly by their arrangement and partly by
repetitions. If these change, it is by instantaneous metamorphosis.
(NEM 4:219)
We form in the imagination some sort of diagrammatic, that is, iconic,
representation of the facts, as skeletonized as possible. The impression
of the present writer is that with ordinary persons this is always a
visual image, or mixed visual and muscular... This diagram, which has
been constructed to represent intuitively or semi-intuitively the same
relations which are abstractly expressed in the premisses, is then
observed, and a hypothesis suggests itself that there is a certain
relation between some of its parts — or perhaps this hypothesis had
already been suggested. In order to test this, various experiments are
made upon the diagram, which is changed in various ways. (CP 2.778)
Diagrammatic reasoning is the only really fertile reasoning. If
logicians would only embrace this method, we should no longer see
attempts to base their science on the fragile foundations of metaphysics
or a psychology not based on logical theory. (CP 4.571)
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